Section: Systems and Control
Tutor: GARATTI SIMONE Major Research topic
:Hierarchical and multilayer structures for large-scale systems
Advisor: SCATTOLINI RICCARDOAbstract:
Over the last decades, the complexity of systems is continuously increasing due to economic reasons and technological advances. It is known that the centralized Model Predictive Control (MPC) solutions for such large-scale systems might result in unacceptable control performance. Moreover, centralized controllers are not scalable and difficult to maintain. For these reasons, in the last twenty years, decentralized and distributed MPC algorithms have been developed with a number of local problems solved in parallel to achieve global or local objectives. An alternative to decentralized and distributed control consists in the use of hierarchical control structures based on MPC. This approach is very powerful especially for control of systems with separable fast and slow dynamics, for the coordination of subsystems and when it is required to consider different objectives in the long term and regulation problems in the short term.
This Thesis addresses the theoretical development of hierarchical and multilayer control algorithms based on MPC for large-scale systems.
In Chapter 2, we develop a two-layer control structure for the coordination of independent linear dynamic systems with input and joint output constraints. At the higher layer, a reduced order dynamic model of the system's components is used to state and solve an economic MPC algorithm in a long time scale. The outcomes of this layer are the components of the control variables to be held constant over the long sampling periods. At the lower layer, decentralized MPC controllers, one for each subsystem, are implemented in a shorter timescale and according to a shrinking horizon strategy to compensate for the model inaccuracies at the high level. The overall convergence, recursive feasibility, as well as the fulfillment of the joint constraints, are obtained under mild assumptions.
A fully scalable hierarchical control scheme for coordination of similar independent systems with joint output and input constraints is presented in Chapter 3. Differently from Chapter 2, a scalable low-dimensional model mapping the common input to the collective output is used at the high layer, this model is easily determined from the impulse responses of the subsystems. The outcome of the high layer is the value of the common input to be held constant and to be distributed among the subsystems based on a specific weight associated with each subsystem. This approach allows to modify the system configuration with time varying weights, in terms of the contribution provided by any subsystem to the overall system performance, and to implement plug-and-play operations. The recursive feasibility is guaranteed also during plug-in and plug-out operations, and the overall convergence of the system output to the set-point is proven.
Finally, in Chapter 4, we extend the hierarchical control structure to large-scale interconnected systems. At the higher layer, a robust centralized MPC algorithm based on a reduced order dynamic model optimizes a long-term performance index, while at the lower layer local MPC regulators, are designed for the full order models of the subsystems to refine the control action computed at the higher layer. The recursive feasibility and robustness of the two layer algorithm are guaranteed and the overall convergence of the state to the steady state is fully discussed.
Several simulation examples are reported to show the effectiveness of all the proposed algorithms.